×

A new approach for describing glass transition kinetics. (English. Russian original) Zbl 1195.82071

Theor. Math. Phys. 163, No. 1, 537-548 (2010); translation from Teor. Mat. Fiz. 163, No. 1, 163-176 (2010).
Summary: We use a functional integral technique generalizing the Keldysh diagram technique to describe glass transition kinetics. We show that the Keldysh functional approach takes the dynamical determinant arising in the glass dynamics into account exactly and generalizes the traditional approach based on using the supersymmetric dynamic generating functional method. In contrast to the supersymmetric method, this approach allows avoiding additional Grassmannian fields and tracking the violation of the fluctuation-dissipation theorem explicitly. We use this method to describe the dynamics of an Edwards-Anderson soft spin-glass-type model near the paramagnet-glass transition. We show that a Vogel-Fulcher-type dynamics arises in the fluctuation region only if the fluctuation-dissipation theorem is violated in the process of dynamical renormalization of the Keldysh action in the replica space.

MSC:

82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] L. F. Cugliandolo, ”Dynamics of glassy systems,” arXiv:cond-mat/0210312v2 (2002).
[2] S. L. Ginzburg, Irreversible Phenomena in Spin Glasses [in Russian] (Contemp. Prob. Phys., Vol. 79), Nauka, Moscow (1989).
[3] D. R. Reichman and P. Charbonneau, J. Stat. Mech., 0505, 05013 (2005).
[4] G. Parisi and N. Sourlas, Phys. Rev. Lett., 43, 744–745 (1979).
[5] J. Kurchan, J. Phys. I (France), 2, 1333–1352 (1992).
[6] L. V. Keldysh, Sov. Phys. JETP, 20, 1018–1026 (1965).
[7] A. Kamenev, ”Many-body theory of non-equilibrium systems,” in: Nanophysics: Coherence and Transport (Volume Session 81 Lect. Notes Les Houches Summer School 2004, H. Bouchiat, Y. Gefen, S. Gueron, G. Montambaux, and J. Dalibard, eds.), Elsevier, Amsterdam (2005), pp. 177–246.
[8] P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A, 8, 423–437 (1973); C. De Dominics, ”Techniques de renormalisation de la théorie des champs et dynamique des phénomènes critiques,” in: Hydrodynamique physique et instabilités (J. Phys. Colloques, Vol. 37, Suppl. C1) (1976), p. C1-247–C1-253.
[9] P. C. Hohenberg and B. I. Halperin, Rev. Modern Phys., 49, 435–479 (1977).
[10] M. N. Vasil’ev, Quantum Field Renormalization Group in the Theory of Critical Behavior and Statistical Dynamics [in Russian], Petersburg Inst. Nucl. Phys., St. Petersburg (1998); English transl.: The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics, Chapman and Hall, New York (2004).
[11] A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions [in Russian], Nauka, Moscow (1982); English transl. prev. ed. (Internat. Ser. Nat. Phil., Vol. 98), Pergamon, Oxford (1979).
[12] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett., 35, 1792–1796 (1975); S. Kirkpatrick and D. Sherrington, Phys. Rev. B, 17, 4384–4403 (1978).
[13] M. Mehta, Random Matrices (Pure Appl. Math., Vol. 142), Elsevier, Amsterdam (2004).
[14] R. L. Stratonovič, Sov. Phys. Dokl., 2, 416–419 (1957); J. Hubbard, Phys. Rev. Lett., 3, 77–78 (1959).
[15] L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian] (Vol. 5 of Course of Theoretical Physics), Nauka, Moscow (1976); English transl. prev. ed., Pergamon, Oxford (1968).
[16] G. Parisi, J. Phys. A, 13, 1101–1112 (1980).
[17] G. Parisi, ”Course 6: Glasses, replicas, and all that,” in: Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter (Les Houches, Vol. 77, J.-L. Barrat et al.), Springer, Berlin (2004), pp. 33–63; arXiv:condmat/0301157v1 (2003).
[18] M. G. Vasin, Theor. Math. Phys., 147, 721–728 (2006). · Zbl 1177.82118
[19] M. V. Feigel’man, A. I. Larkin, and M. A. Skvortsov, Phys. Rev. B, 61, 12361–12388 (2000).
[20] I. S. Beloborodov, A. V. Lopatin, G. Schwiete, and V. M. Vinokur, Phys. Rev. B, 70, 073404 (2004).
[21] I. S. Burmistrov and N. M. Chtchelkatchev, Phys. Rev. B, 77, 195319 (2008).
[22] S. Chandrasekhar, Rev. Modern Phys., 15, 1–89 (1943). · Zbl 0061.46403
[23] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics [in Russian], GIFML, Moscow (1962); English transl., Prentice-Hall, New York (1963). · Zbl 0135.45003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.